Hello The excellent adapt package integrates over multi-dimensional hypercubes.
I want to integrate over a multidimensional simplex. Has anyone implemented such a thing in R? I can transform an n-simplex to a hyperrectangle but the Jacobian is a rapidly-varying (and very lopsided) function and this is making adapt() slow. [ A \dfn{simplex} is an n-dimensional analogue of a triangle or tetrahedron. It is the convex hull of (n+1) points in an n-dimensional Euclidean space. My application is a variant of the Dirichlet distribution: With p~D(a), if length(p) = n+1 then the requirement that all(p>0) and sum(p)=1 mean that the support of the Dirichlet distribution is an n-simplex. ] -- Robin Hankin Uncertainty Analyst National Oceanography Centre, Southampton European Way, Southampton SO14 3ZH, UK tel 023-8059-7743 ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.